Dynamic treatment of vibrational energy relaxation in a heterogeneous and fluctuating environment

TL;DR

This paper presents a computational method that models vibrational energy relaxation in fluctuating environments, revealing biphasic relaxation behavior consistent with experimental observations for amide I modes.

Contribution

It extends previous perturbation theory approaches by incorporating dynamic fluctuations of vibrational frequencies along MD trajectories within the vibrational adiabatic approximation.

Findings

Relaxation occurs in two phases: a rapid initial phase and a slower subsequent phase.

Including dynamic fluctuations significantly alters the predicted vibrational energy relaxation.

The theoretical results show excellent agreement with experimental data for N-methylacetamide.

Abstract

A computational approach to describe the energy relaxation of a high-frequency vibrational mode in a fluctuating heterogeneous environment is outlined. Extending previous work [H. Fujisaki, Y. Zhang, and J.E. Straub, J. Chem. Phys. {\bf 124}, 144910 (2006)], second-order time-dependent perturbation theory is employed which includes the fluctuations of the parameters in the Hamiltonian within the vibrational adiabatic approximation. This means that the time-dependent vibrational frequencies along an MD trajectory are obtained via a partial geometry optimization of the solute with fixed solvent and a subsequent normal mode calculation. Adopting the amide I mode of N-methylacetamide in heavy water as a test problem, it is shown that the inclusion of dynamic fluctuations may significantly change the vibrational energy relaxation. In particular, it is found that relaxation occurs in two phases, because for short times ($\lesssim$ 200 fs) the spectral density appears continuous due to the frequency-time uncertainty relation, while at longer times the discrete nature of the bath becomes apparent. Considering the excellent agreement between theory and experiment, it is speculated if this behavior can explain the experimentally obtained biphasic relaxation the amide I mode of N-methylacetamide.